dc.contributor.author Carmona Mejías, Ángeles dc.contributor.author Encinas Bachiller, Andrés Marcos dc.contributor.author Mitjana Riera, Margarida dc.contributor.author Monsó Burgués, Enrique P.J. dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.contributor.other Universitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada dc.date.accessioned 2019-10-02T08:31:03Z dc.date.available 2019-10-02T08:31:03Z dc.date.issued 2019 dc.identifier.citation Carmona, A. [et al.]. Generalizing the bottleneck matrix. A: Meeting of the International Linear Algebra Society. "Libro de ACTAS- 22nd Conference of the International Linear Algebra Society (ILAS)". 2019, p. 1-6. dc.identifier.uri http://hdl.handle.net/2117/169044 dc.description.abstract Given the Laplacian matrix associated to a weighted graph and given x a single vertex of it, the bottleneck matrix (related to x) is the inverse matrix of the sub matrix of the Laplacian obtained by eliminating the row and the column corresponding to x. The bottleneck matrix is used to calculate the group inverse of the initial Laplacian matrix, for instance. In this work we have managed to generalize this situation twofold: in the sense of considering symmetric M–matrices related to Schr¨odinger operators acting on networks (doubly weighted graphs, where not only edges but also vertices are discriminated) and also by using sub-matrices of the initial one in which two, three or more rows and columns are erased, those corresponding to two, three or more vertices. We conceive that every symmetric M–matrix corresponds to a network where both a conductance on the edges and a weight on the vertices are introduced. Solving boundary value problems for Schr¨odinger’s operators throughout the whole network or just a part of it, we find the relation between the corresponding group inverse and inverse matrices respectively. Since the part of the network to be considered is arbitrary, the reduction in the order of the matrices is also arbitrary. The work is finished by exposing the application of our result to the calculation of the Green function of a path. dc.format.extent 6 p. dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Matrices dc.subject.other Bottleneck matrix dc.subject.other Schrodinger operator dc.subject.other Green’s function dc.subject.other M-matrix dc.subject.other Group–inverse matrix dc.title Generalizing the bottleneck matrix dc.type Conference report dc.subject.lemac Matrius (Matemàtica) dc.contributor.group Universitat Politècnica de Catalunya. MAPTHE - Anàlisi matricial i Teoria Discreta del Potencial dc.rights.access Open Access local.identifier.drac 25638663 dc.description.version Postprint (published version) local.citation.author Carmona, A.; Encinas, A.; Mitjana, M.; Monso, E. local.citation.contributor Meeting of the International Linear Algebra Society local.citation.publicationName Libro de ACTAS- 22nd Conference of the International Linear Algebra Society (ILAS) local.citation.startingPage 1 local.citation.endingPage 6
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